Post Reply 
 
Thread Rating:
  • 0 Votes - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Mankind is building "Gods"
12-01-2017, 09:26 AM (This post was last modified: 12-01-2017 09:31 AM by %mindless_detector%.)
Post: #1
Mankind is building "Gods"
[Image: DaQ6mM1.png]

Like Sam Harris the atheist says, we are building Gods.

  1. The God that he is referring to is quite disparate from the theistic God.
  2. Of course, I am an atheist, and like Sam, I tend to discuss the inevitable emergence of this super-intelligent "God". (See this paper to see how it is possible to support "God" concept while being an atheist.)
  3. The God that Sam is referring to, is all about artificial general intelligence.


Anyway, it would seem "God" as it relates to artificial intelligence, has been on github since 2016.

Thanks for reading.

Signature: I am interested in completing a novel learning model I call the "Supersymmetric Artificial Neural Network". (See this easy overview)
Find all posts by this user
Quote this message in a reply
12-01-2017, 06:26 PM (This post was last modified: 12-01-2017 06:43 PM by Amememhab.)
Post: #2
RE: Mankind is building "Gods"
Awful big image spread there. Please resize to ≈500px width or less if you can, else the reader can’t see the whole image, but must use the scroll bars to scan its parts. At any rate, one cannot raise a number to the power ∞. The expression

C^(∞π)

is undefined; it has no numerical value. Hence, so is C^(∞π)R^(kπ). If C > 0, then C^(∞p) –> ∞ for all p > 0. If C < 0, the expression is still undefined. If C =0, undefined once again, yet limit (0^n) as n goes to infinity is zero. Using the methods of calculus, you can attempt to evaluate

limit as n –> ∞ of (f(n))^n

in the cases where the limit is of form 0^∞. This limit may or may not exist in a particular case; there are some important limits of this form, however. If f(n) itself does not approach zero as n –> ∞, then the limit will not exist, as the power will grow out of bounds. Thus in your image, if C is a nonzero constant, no limit of form C^∞ can exist as it grows out of bounds.

If you have the limit of a product

limit as n –> ∞ of C(n)^(πn) x R(n) ^(πn),

you may attempt to evaluate it if it’s of form 0^∞ x 0^∞, if upon reduction you reach an equivalent limit of form 0 x ∞. Of course, this limit may or may not exist.

Find all posts by this user
Quote this message in a reply
12-01-2017, 11:19 PM (This post was last modified: 12-01-2017 11:25 PM by %mindless_detector%.)
Post: #3
RE: Mankind is building "Gods"
(12-01-2017 06:26 PM)Amememhab Wrote:  At any rate, one cannot raise a number to the power ∞. The expression

C^(∞π)

is undefined; it has no numerical value.

You are demonstrably wrong.

  1. I've left out the remainder of your original quote, as it stemmed from your error as quoted above.
  2. Your error is that C^∞..(R^k..) is not "undefined", as you falsely presented.
  3. C^∞(R^k) is a standard way to define supermanifolds:

    See: https://en.wikipedia.org/wiki/Supermanif...as_a_sheaf

    [Image: 8DO8Ile.png]

Signature: I am interested in completing a novel learning model I call the "Supersymmetric Artificial Neural Network". (See this easy overview)
Find all posts by this user
Quote this message in a reply
12-02-2017, 01:48 PM (This post was last modified: 12-02-2017 02:41 PM by Amememhab.)
Post: #4
RE: Mankind is building "Gods"
(12-01-2017 11:19 PM)%mindless_detector% Wrote:  You are demonstrably wrong...Your error is that C^∞..(R^k..) is not "undefined", as you falsely presented.

Negatory! I see no C^(∞π)R^(kπ) in the Wikipedia article on supermanifolds; I see only that this mathematical object is “isomorphic to C^∞ x R(^p) x Л(ξ sub i, i = 1 to q),” where the latter is a Grassmann algebra on q generators. Don’t ask me more about it; I’m as lost here as you are! There seems to be a noncommutative division ring involved. Supermanifolds sway mainly the wide eyes of young smart physicists who examine the whole-integer spin of bosons and half-integer spin of fermions. That’s the best I can do for you by way of explication.

We’re not discussing manifolds, however, even if a fascinating example is the 3-D torus where you can see the back and top of your head and the soles of your feet all at the same time! I spent years earning a bachelor of science in mathematics, Mindless Detector. I hope I still retain driblets of that education 30 years ago. You’re not gonna awe me as easily as you think.
~ Tongue

“A Few of My Favorite Spaces: The Three-Torus:
Living in a three-dimensional torus would be a narcissist's dream.”
Scientific American blogs, Dec. 30, 2015
https://blogs.scientificamerican.com/roo...ree-torus/

If C is a nonzero constant and you keep hiking its exponent, the result gets larger in magnitude. Just think

10^1 = 10 which has one digit “zero” at its end,
10^10 = 10,000,000,000 which has ten of them,
10^100 = googol, which has a hundred of them, and

10^(10^100), the googolplex which has so many zeros (a googol of goose eggs) our observable astronomical universe is too small for you to cram them all in! Milton Sirotta, an imaginative 9-year old boy, named the integer 10^100 a “googol” back in the 1950s, whence his uncle “plexed” it.

History of Googol
MRob
https://mrob.com/pub/num/n-e100_1-googol...lplex.html

The constant π doesn’t really matter here. The only way you can pull a finite rabbit of form C^∞ out of a hat is if C is a function of x, and you take

limit as x –> ∞ C(x)^x

which is most commonly done by writing y = C(x)^x and taking the logarithm of both sides to obtain

ln y = x ln C(x)

The right side of this puppy, with a smidgeon of luck, may reduce to a limit of form 0 x ∞ which you can evaluate, although it need not. For C(x) must “sprint toward zero” faster than the exponential tries to elevate it to infinity atop Satyros’s mountain! After you’ve taken the log of both sides, see for instance Protter & Protter (1988), Calculus with Analytic Geometry, 4ed., Jones & Bartlett Learning, p. 379, “Indeterminate Forms.”

A 0^∞ limit problem, after taking logs to make it of form 0 x ∞, can be evaluated by taking the reciprocal of the function which goes to infinity, applying L’Hospital’s Rule to the resulting 0/0 form. Whee! I feel like a little boy seated beneath the Christmas tree again!

Protter & Protter (1988)
Calculus with Analytic Geometry, 4ed
Google Books bibliographic record
https://books.google.com/books?id=jTmuOwwGDwoC

While perusing this textbook, Mindless, don’t neglect to flip to the section, “Translation of Axes,” p. 476, which shall launch you on your way toward the coordinate conversions you’ll need for the noncommutative manifolds you know so much about.

Yet please, don’t convert yourself from wise Egyptian Nile Valley baboon to silly American buffoon by posting a screen clip with a Wikipedia on those noncommutative manifolds. I never studied them; they’re graduate school stuff many a twentysomething freshface sweats over ere oral examinations for the PhD. And they look pretty damn hard; miserable Amememhab having taken 400mg of ibuprofen for the headache he got just by looking at the beastie in the Wiki.
~ Big Grin

And please, don’t try to lead me down a primrose path on limit processes learnt in fall semester freshman calculus! Go to your community college instead, and take an evening course in calc. It’ll do your noggin a bit of eggnog good this holiday season!

As an overaged math grad, I’ve relished destroying you mathematically on this forum, Mindless Detector, but it’s not personal. Most of us have trouble with math; kids aren’t taught it anymore and I’m steadily forgetting mine. I was never more than a student of math; I lack a PhD. And I’m sure you’re a swell fellow despite. Happy holidays, Detector! And stay warm beside the fireplace with cheer, if you live in a summer-winter climate where it gets cold!
~ Smile
Find all posts by this user
Quote this message in a reply
12-02-2017, 05:10 PM
Post: #5
RE: Mankind is building "Gods"
demonstrably wrong... falsely presented...

BOOM HEADSHOT! Big Grin

Don't cling to a mistake just because you spent a lot of time making it
Find all posts by this user
Quote this message in a reply
12-02-2017, 09:53 PM (This post was last modified: 12-02-2017 10:11 PM by %mindless_detector%.)
Post: #6
RE: Mankind is building "Gods"
(12-02-2017 01:48 PM)Amememhab Wrote:  
(12-01-2017 11:19 PM)%mindless_detector% Wrote:  You are demonstrably wrong...Your error is that C^∞..(R^k..) is not "undefined", as you falsely presented.

Negatory! I see no C^(∞π)R^(kπ) in the Wikipedia article on supermanifolds; I see only that this mathematical object is “isomorphic to C^∞ x R(^p) x Л(ξ sub i, i = 1 to q),” where the latter is a Grassmann algebra on q generators. Don’t ask me more about it; I’m as lost here as you are! There seems to be a noncommutative division ring involved. Supermanifolds sway mainly the wide eyes of young smart physicists who examine the whole-integer spin of bosons and half-integer spin of fermions. That’s the best I can do for you by way of explication.

We’re not discussing manifolds, however, even if a fascinating example is the 3-D torus where you can see the back and top of your head and the soles of your feet all at the same time! I spent years earning a bachelor of science in mathematics, Mindless Detector. I hope I still retain driblets of that education 30 years ago. You’re not gonna awe me as easily as you think.
~ Tongue

I wasn't attempting to awe anybody.
  1. You made a false opening statement (in reply 2) that "it is impossible to raise a value to ∞".

    I just showed quickly (by standard supermanifold notation in reply #3), that your statement was false.
  2. The π notation is a novel modification of the standard supermanifold notation. It is a treatment to indicate reinforcement learning.

    It is legal to attribute π symbols wrt to equations, to denote some reinforcement learning policy.

    A quick example (by Google Deepmind) of π treatment is seen in the third to last point before the conclusion section in this url.

    This treatment does not suddenly remove the fact that your original statement is wrong, as shown in point 1 above.
  3. You "spending years in mathematics" does not excuse you from your error, as seen in point 1. It is unrealistic to expect any one person to be "omniscient" of the broad scope of mathematics, so your error is understandable. Likewise my focus on mathematics is quite narrow, and largely encompasses math respect to machine learning.

    Machine learning related math is a very small subset of the grand landscape, but I knew about supermanifold notation (which is not common in machine learning) because I took interest in Edward Witten's work years ago.

Signature: I am interested in completing a novel learning model I call the "Supersymmetric Artificial Neural Network". (See this easy overview)
Find all posts by this user
Quote this message in a reply
12-03-2017, 05:42 PM
Post: #7
RE: Mankind is building "Gods"
(12-02-2017 05:10 PM)Herminator Wrote:  BOOM HEADSHOT! Big Grin

Ja. So descendeth this thread into inanity! And I bet the headshot decapitating a hapless warrior when his head protruded out the hatch of his tank was an RPG fired at the tank itself. At least the other crew in the tank survived, armored division personnel having not to worry an RPG might hull their tank, yet if the RPG bursts against its side, the fella on the other side of its metal armor plate will get a nice concussion and ears ringing ’til next Thursday. And their tank will have to go to the shop with a nice dent—a plate the mechanics will need to replace.

Thanks, Herm, for your morsels of moral support!
~ Big Grin

(12-02-2017 09:53 PM)%mindless_detector% Wrote:  It is legal to attribute π symbols wrt to equations, to denote some reinforcement learning policy.
...
Machine learning related math is a very small subset of the grand landscape, but I knew about supermanifold notation (which is not common in machine learning) because I took interest in Edward Witten's work years ago.

Sure,

π = 3.1415926535...

a mathematical constant, a number now known not only to be irrational, as √2 was so known to the Pythagorean Greek mathematician-mystics of 500 BCE introducing the term “incommensurability” in their written proof, but transcendental as well, that is, irreducible to radicals, unlike √2. π can be plugged in as coefficient in any equation you like. Mindless Detector, don’t you feel like a bodhisattva, resting cross-legged upon a cloud of transcendental real numbers, which “outnumber” their algebraic counterparts?

However, recall that ∞ is not a number. The expression

8^∞

is undefined. Sorry, guy, I hate to disturb your tranquil rest, but that’s a fact. I won’t argue about it with you. If it’s defined, then please tell me its value. We calc students may write

8^∞ = ∞

to mean that

limit as x –> ∞ 8^x = ∞,

that is, any sequence building this limit will lack an upper bound. Dear Mindless, when you utter statements such as

(12-02-2017 09:53 PM)%mindless_detector% Wrote:  A quick example (by Google Deepmind) of π treatment is seen in the third to last point before the conclusion section in this url.

your lack of college freshman mathematics shows plainly to me.

Bill Cherowitzo
Geometry in Plato’s Academy
“Let None Ignorant of Geometry Enter My Door,”
University of Colorado at Denver
http://www.math.ucdenver.edu/~jloats/APr...10.ppt.pdf

If you’re reading Edward Witten’s string theories or his M-theory without a freshman calculus, then my hat tips to you. I don’t understand string theory, other than as a sort of piano string in which the vibrational modes generate the elementary particles of our cosmos. But let’s return to limit basics. We can write all of

limit as x –> ∞ f(x) = a
limit as x –> ∞ f(x) = ∞
limit as x –> a f(x) = ∞

to indicate the presence or absence of upper and lower bounds on sequences which lead to these limits. In practice, we usually don’t write out a sequence, but use algebraic manipulation of f(x) or the differentiation formulas we’ve learnt as in L’Hospital’s Rule. Remember that Tasmanian devil?

In other words, until you enroll in college and take some math, don’t argue that subject with Amememhab. You’ll quickly sink in the unstable Noah’s Ark if you do. You can, however, argue other topics with me. I know very little about computer algorithms for machine learning, for instance, although I’ve heard of the “neural network” with its weighted nodes. I doubt supermanifolds are involved, yet if they are, please intelligence me regarding it.

You, Mindless, have just informed me that computers can now play the Chinese-Japanese game of Go like an 8-dan in the Nihon Ki-in. I can play both Chess and Go, yet my game in both is awful. I have a Chess software on my PC, Chess King 3: “Your coach to improving your game.” I regularly lose to it. I’ll never be a grandmaster. And I don’t know how hane (diagonal placement of next stone from yours, but orthogonally adjacent to opponent’s) works in Go, nor any tesuji to sic on the other player. The Nihon Ki-in, Japan’s professional Go league, does know such things, however. Here they are:

Nihon Ki-in of Japan
https://www.nihonkiin.or.jp/english/

I’m somewhat better at Chess than at Go. Experts can play Chess games mentally, without a board and pieces, their memory telling them which square each piece stands on. I can follow the first four or five moves from the opening setup mentally, but lose track of the pieces thereafter. I’ll never reach a 2100-Expert ELO; my ELO rating, once around 1650, has declined, probably to 1475, as I don’t play regularly enough, nor study books such as I. A. Horowitz’s Chess Openings: Theory and Practice.

I. A. Horowitz, 2015
Chess Openings: Theory and Practice
https://books.google.com/books/about/Che...XYsgEACAAJ

I wish you a happy holiday season, Mindless Detector. Maybe computers really will outsmart us on some day, dispensing with the very need to have human beings walking this Earth, but I’ll likely be safe in my coffin by then.
~ Smile
Find all posts by this user
Quote this message in a reply
12-04-2017, 10:41 AM (This post was last modified: 12-04-2017 10:42 AM by muhammad_isa.)
Post: #8
RE: Mankind is building "Gods"
(12-03-2017 05:42 PM)Amememhab Wrote:  ...
However, recall that ∞ is not a number...

No .. it's not even a big number Big Grin

Is 1^1/2 a number ie. is a complex number a number?

He maketh me to lie down in green pastures: He leadeth me beside the still waters.
Find all posts by this user
Quote this message in a reply
12-04-2017, 03:33 PM (This post was last modified: 12-04-2017 03:35 PM by Herminator.)
Post: #9
RE: Mankind is building "Gods"
(12-04-2017 10:41 AM)muhammad_isa Wrote:  
(12-03-2017 05:42 PM)Amememhab Wrote:  ...
However, recall that ∞ is not a number...

No .. it's not even a big number Big Grin

Is 1^1/2 a number ie. is a complex number a number?

1^1/2 is the square root of 1, which is a number, and definitely is not a complex number.

You know what I have told you about math Isa...

Don't cling to a mistake just because you spent a lot of time making it
Find all posts by this user
Quote this message in a reply
12-04-2017, 03:55 PM
Post: #10
RE: Mankind is building "Gods"
(12-04-2017 03:33 PM)Herminator Wrote:  
(12-04-2017 10:41 AM)muhammad_isa Wrote:  
(12-03-2017 05:42 PM)Amememhab Wrote:  ...
However, recall that ∞ is not a number...

No .. it's not even a big number Big Grin

Is 1^1/2 a number ie. is a complex number a number?

1^1/2 is the square root of 1, which is a number, and definitely is not a complex number.

You know what I have told you about math Isa...

You would think fractions would be pretty basic.... Isa is restricted to whole numbers only... Tongue

----------------------
Does anyone know where the love of God goes
when the waves turn the minutes to hours?
Find all posts by this user
Quote this message in a reply
Post Reply 




User(s) browsing this thread: 2 Guest(s)